{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T08:15:47Z","timestamp":1783325747835,"version":"3.54.6"},"reference-count":36,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T00:00:00Z","timestamp":1778457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Linkage disequilibrium (LD), logarithm of the odds (LOD), and recombination frequency (Rf) have long been measured independently. However, their relationship in viral haploid recombination has not been fully understood due to the unavailability of population-wide sequencing data until recently. Here, we provide the first mathematical model of haploid LOD and Rf, LODF, and RfF, using recombinant single-nucleotide polymorphism pairs (RSPs) as natural genomic markers of LD in monkeypox\/mpox virus (MPXV) Ib sequences during the 2023 to 2025 outbreak. The recombinant haplotype allele frequency (Af) includes recombinant progeny (AfF for haploid population), while RfF is the measured non-progeny AfF when recombination breaks linkage. LODF and RfF are in a decaying exponential relationship, showing that recombination events lower LODF, and newly arising RSPs are strongly favored in the population. Our data reveal that Haploview's LODH vs AfH and our LODF vs AfF increase in a growing power relationship, suggesting that 8,247 RSPs out of 8,587 RSPs show strong evidence of LD and are related to historical recombination. We derived a new mathematical model to determine the maximum bound of historical recombination\/progeny frequency, AfH,max, at any given LODH. This serves as a critical reliability marker for RSPs because AfH,max tests the strength of the binomial connection between LOD and Af. Taken together, observing recombination drive retention of RSPs containing high LD indicates that LODF and AfF have a strong association in the MPXV Ib viral population. These different LD methods provide powerful and complementary tools for scoring genetic linkage of haploid population genetics and evolution.<\/jats:p>","DOI":"10.1093\/genetics\/iyag118","type":"journal-article","created":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T21:01:02Z","timestamp":1778533262000},"source":"Crossref","is-referenced-by-count":0,"title":["A new mathematical model for genetic linkage and recombination of haploid virus populations"],"prefix":"10.1093","volume":"233","author":[{"given":"Patrick J","family":"Feehley","sequence":"first","affiliation":[{"name":"Rita Rossi Colwell Center Auxergen Inc., , 701 E. Pratt Street, Baltimore, MD 21202 ,","place":["United States"]},{"name":"Auxergen S.r.l., Tecnopolis PST, University of Bari , Valenzano, BA 70010 ,","place":["Italy"]},{"name":"Department of Biophysics, Johns Hopkins University , Baltimore, MD 21218 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael C","family":"Feehley","sequence":"additional","affiliation":[{"name":"Rita Rossi Colwell Center Auxergen Inc., , 701 E. Pratt Street, Baltimore, MD 21202 ,","place":["United States"]},{"name":"Auxergen S.r.l., Tecnopolis PST, University of Bari , Valenzano, BA 70010 ,","place":["Italy"]},{"name":"Department of Biophysics, Johns Hopkins University , Baltimore, MD 21218 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zih-Yu","family":"Hsieh","sequence":"additional","affiliation":[{"name":"Rita Rossi Colwell Center Auxergen Inc., , 701 E. Pratt Street, Baltimore, MD 21202 ,","place":["United States"]},{"name":"Department of Mathematics, University of California , Santa Barbara, CA 93106 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-5570-4369","authenticated-orcid":false,"given":"Alex T","family":"Poyer","sequence":"additional","affiliation":[{"name":"Department of Software Engineering, Rochester Institute of Technology , Rochester, NY 14623 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gregory P","family":"Contreras","sequence":"additional","affiliation":[{"name":"Rita Rossi Colwell Center Auxergen Inc., , 701 E. Pratt Street, Baltimore, MD 21202 ,","place":["United States"]},{"name":"Auxergen S.r.l., Tecnopolis PST, University of Bari , Valenzano, BA 70010 ,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5333-5486","authenticated-orcid":false,"given":"Ting-Yu","family":"Yeh","sequence":"additional","affiliation":[{"name":"Rita Rossi Colwell Center Auxergen Inc., , 701 E. Pratt Street, Baltimore, MD 21202 ,","place":["United States"]},{"name":"Auxergen S.r.l., Tecnopolis PST, University of Bari , Valenzano, BA 70010 ,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,5,11]]},"reference":[{"key":"2026070603272731400_iyag118-B1","doi-asserted-by":"publisher","first-page":"iyac127","DOI":"10.1093\/genetics\/iyac127","article-title":"Heterogeneity in viral populations increases the rate of deleterious mutation accumulation","volume":"222","author":"Allman","year":"2022","journal-title":"Genetics"},{"key":"2026070603272731400_iyag118-B2","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1111\/j.2517-6161.1949.tb00028.x","article-title":"Statistical inference","volume":"11","author":"Barnard","year":"1949","journal-title":"J R Stat Soc Series B Stat Methodol."},{"key":"2026070603272731400_iyag118-B3","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1093\/bioinformatics\/bth457","article-title":"Haploview: analysis and visualization of LD and haplotype maps","volume":"21","author":"Barrett","year":"2005","journal-title":"Bioinformatics"},{"key":"2026070603272731400_iyag118-B4","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1159\/000130612","article-title":"The interpretation of LODs in linkage analysis","volume":"16","author":"Edwards","year":"2008","journal-title":"Cytogenet Cell Genet."},{"key":"2026070603272731400_iyag118-B5","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1002\/gch2.1018","article-title":"Data, disease and diplomacy: GISAID\u2019s innovative contribution to global health","volume":"1","author":"Elbe","year":"2017","journal-title":"Glob Chall"},{"key":"2026070603272731400_iyag118-B6","doi-asserted-by":"publisher","author":"Feehley","DOI":"10.1101\/2025.08.11.25333454"},{"key":"2026070603272731400_iyag118-B7","doi-asserted-by":"publisher","first-page":"221","DOI":"10.3390\/v10050221","article-title":"Within-host recombination in the foot-and-mouth disease virus genome","volume":"10","author":"Ferretti","year":"2018","journal-title":"Viruses"},{"key":"2026070603272731400_iyag118-B8","doi-asserted-by":"publisher","first-page":"2225","DOI":"10.1126\/science.1069424","article-title":"The structure of haplotype blocks in the human genome","volume":"296","author":"Gabriel","year":"2002","journal-title":"Science"},{"key":"2026070603272731400_iyag118-B9","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1016\/j.ymeth.2021.09.005","article-title":"Characterisation of SARS-CoV-2 clades based on signature SNPs unveils continuous evolution","volume":"203","author":"Ghosh","year":"2022","journal-title":"Methods"},{"key":"2026070603272731400_iyag118-B10","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1128\/CMR.00075-13","article-title":"Whole-genome sequencing in outbreak analysis","volume":"28","author":"Gilchrist","year":"2015","journal-title":"Clin Microbiol Rev."},{"key":"2026070603272731400_iyag118-B11","doi-asserted-by":"publisher","first-page":"772","DOI":"10.1093\/molbev\/mst010","article-title":"MAFFT multiple sequence alignment software version 7: improvements in performance and usability","volume":"30","author":"Katoh","year":"2013","journal-title":"Mol Biol Evol."},{"key":"2026070603272731400_iyag118-B12","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1093\/genetics\/61.4.893","article-title":"The number of heterozygous nucleotide sites maintained in a finite population due to steady flux of mutations","volume":"61","author":"Kimura","year":"1969","journal-title":"Genetics"},{"key":"2026070603272731400_iyag118-B13","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1038\/9642","article-title":"Prospects for whole-genome linkage disequilibrium mapping of common disease genes","volume":"22","author":"Kruglyak","year":"1999","journal-title":"Nat Genet."},{"key":"2026070603272731400_iyag118-B14","doi-asserted-by":"publisher","first-page":"101511","DOI":"10.1016\/j.nmni.2024.101511","article-title":"Identification of clade-defining single nucleotide polymorphisms for improved rabies virus surveillance","volume":"62","author":"Kumar","year":"2024","journal-title":"New Microbes New Infect."},{"key":"2026070603272731400_iyag118-B15","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1093\/genetics\/49.1.49","article-title":"The interaction of selection and linkage. 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